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    OlympiadMediumGeometry7–9

    The Ant on the Box

    A Formiga na Caixa

    A closed box measures 3 \times 4 \times 12 cm. An ant walks on the surface of the box from one corner to the corner diagonally opposite. What is the length of the shortest such walk?

    A path over two faces becomes a straight segment once the two faces are flattened into one plane; there is more than one way to flatten them.

    Solution

    Step 1 of 6

    1. 1.Unfold the two faces the ant crosses into a single rectangle. The straight segment joining the corners is then the shortest path across those faces, and there are three ways to pair the dimensions: